In-plane anomalous Hall effect associated with orbital magnetization

Modern theoretical formulation based on the Berry curvature has revealed potential that even in-plane magnetic field can induce anomalous Hall effect (AHE). However, experimental efforts to observe such a Hall signal are currently very limited and a different scenario has been proposed for each. Among them, orbital magnetization by orbital motion of electrons is essentially important when considering intrinsic AHE, as modernly formulated as a quantum geometric tensor in the Středa formula. The orbital magnetization may not be aligned in the field direction even after the spin magnetization has saturated, although it is usually very small in total magnetization. In simple magnetic Weyl semimetals, for example, the orbital magnetization is parallel and proportional to Weyl points splitting.

Here we report the observation of in-plane AHE in magnetic Weyl semimetals and discuss its possible origins based on symmetry requirements and effective models. Observed large in-plane AHE with three-fold rotational symmetry on a D_3d principal plane can be understood in terms of out-of-plane Weyl points splitting or orbital magnetization induced by in-plane magnetic field. This is expected from the presence of a cross term added in the Weyl Hamiltonian and also confirmed by model calculations.

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[2] N. Ito and K. Nomura, J. Phys. Soc. Jpn. 86, 063703 (2017)